Question: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 2x - 1$ and $ JT = 3x - 10$ Find $CT$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {2x - 1} = {3x - 10}$ Solve for $x$ $ -x = -9$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 2({9}) - 1$ $ JT = 3({9}) - 10$ $ CJ = 18 - 1$ $ JT = 27 - 10$ $ CJ = 17$ $ JT = 17$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {17} + {17}$ $ CT = 34$